In 2005, U.S. households saved less than 2 cents of every dollar they could spend

1.8% The personal saving rate in the third quarter of 2005, its lowest quarter since 1970

In the 1970s households put aside about 12 cents of each dollar. By 2008 they owed almost a year of GDP. Yet their wealth, relative to their income, kept rising. Were they reckless, or were they doing the arithmetic of a lifetime?

Open with the number. It is the lowest quarterly value of the personal saving rate in the notebook’s Fig. 4: 1.8 percent in 2005Q3 (the monthly low is 1.4 percent in July 2005). The 1970s average was 12.2 percent.

Consumption is more than two-thirds of GDP, the biggest piece of spending in the economy. Until now the book treated it simply: a fixed share of income in the Solow model, a fixed share of potential output in the short-run model. This chapter makes it a choice.

Ask the room: think of your own spending this year. Is it tied to what you earn this year, or to what you expect to earn over your life? Students usually spend more than they earn. Why is that sensible?

Today: three questions

• What does a household’s budget look like over a whole life? Total wealth, diminishing marginal utility and the wish to smooth.
• How does a household split its wealth between today and the future? The Euler equation, permanent income, borrowing limits and risk.
• What do debt, saving and wealth show in the data? The U.S. since 1970 and dozens of other countries; then three policy questions.

These are the three acts of the deck and the three branches of the mind map on the title slide.

The headline result: households spend out of lifetime wealth, not this year’s income, so they smooth. Most of a windfall is saved, and interest rates track growth. But borrowing limits and risk make many households spend almost every extra dollar, and that is why the timing of taxes and transfers can matter.

The model has one character, Irving, named after the economist Irving Fisher. He is the “household” of the chapter.

A lifetime budget

Act I

Irving plans for two periods, and can borrow or save at the real rate \(R\)

\[c_{\text{today}} + \underset{\text{saving today}}{(f_{\text{future}} - f_{\text{today}})} = y_{\text{today}}\]

\[c_{\text{future}} = y_{\text{future}} + (1+R)\,f_{\text{future}}\]

• \(f\): financial wealth; \(y\): labor income; \(c\): consumption.
• Each line: spending plus saving equals income, one period at a time.
• Saving can be negative: \(f_{\text{future}} < 0\) is a loan, repaid with interest.

Spending in a period need not match income in that period, as long as the loan is repaid.

Assumptions 1 to 3 of the Model overview. Time has two periods, today and the future. The future is the last period of Irving’s life, so he leaves nothing behind.

Today: Irving starts with financial wealth f_today and earns y_today. What he does not spend raises his financial wealth to f_future. In the future: he earns y_future, gets back his savings with interest, (1 + R) f_future, and spends it all.

He can save or borrow as much as he wants at the same real interest rate R. Act II drops this assumption.

Ask: in which period would a student want to borrow? (Today, when income is low.)

Two budgets merge into one: the present value of spending equals total wealth

\[c_{\text{today}} + \frac{c_{\text{future}}}{1+R} \;=\; \underset{\text{financial wealth}}{f_{\text{today}}} \;+\; \underset{\text{human wealth}}{y_{\text{today}} + \frac{y_{\text{future}}}{1+R}} \;\equiv\; \bar{X}\]

• Solve the future budget for \(f_{\text{future}}\) and put it into today’s budget: one intertemporal budget constraint.
• Dividing by \(1+R\) turns a future amount into a present value.
• Human wealth is the present value of labor income. For most young people it is almost all their wealth.

The budget line has slope \(-(1+R)\): one unit consumed today costs \(1+R\) units later.

Step 1 of the Model overview. From the future budget, f_future = (c_future − y_future)/(1 + R). Substitute into today’s budget and move the income terms and f_today to the right. The result is equation (2) of the book chapter.

Present value: one dollar saved today grows to 1 + R dollars, so 1 + R dollars in the future are worth one dollar now. Both sides of the equation are present values: the left side of spending, the right side of resources.

The bar over X marks a number Irving takes as given: he cannot change his total wealth, only how he spends it.

In a diagram with c_today across and c_future up, the budget is the straight line c_future = (1 + R)(X̄ − c_today). The price of consumption today, in units of future consumption, is 1 + R.

Full derivation: the book chapter’s Model overview.

A student with a small income and a big future is wealthy

Baseline Irving	\(f_{\text{today}}\)	\(y_{\text{today}}\)	\(y_{\text{future}}\)	total wealth \(\bar{X}\)
\(R = 0\)	0	1	5	6.00
\(R = 0.05\)	0	1	5	5.762

• One unit is 10,000 dollars: Irving looks like a student who expects to earn much more later.
• All his wealth is human wealth. A higher \(R\) shrinks it, because future income is discounted more.
• With \(R = 0\) and \(\beta = 1\) he will spend 3 today, though he earns 1: he borrows 2.

What Irving can afford over his life is set by \(\bar{X}\), not by this year’s paycheck.

Numbers: the notebook’s shared baseline (the “model in code” cell): total wealth 6.00 (financial 0.00, human 6.00); consumption 3.00 today and 3.00 in the future; saving today −2.00, so Irving borrows. With R = 0.05: X̄ = 1 + 5/1.05 = 5.762.

The textbook gives no numbers for its diagrams. These are the book chapter’s illustrative values, used in every figure of the notebook.

The last bullet is a preview: we derive the “half of total wealth” rule in Act II. For now, notice that a plan of 3 and 3 is affordable: 3 + 3 = 6 = X̄ at R = 0.

Ask: who in this room has human wealth larger than financial wealth? (Almost everyone.)

Utility

How much does one more unit of consumption add to Irving’s happiness, and does it depend on how much he already has?

With \(u(c) = \log c\), going from 1 to 2 units adds 0.69 of utility. Will going from 8 to 9 units add more, the same, or less? Write down a number.

Ask students to commit to a number before the reveal. Some will say “the same: one unit is one unit”. Others will guess “less”, but not by how much.

Flow utility u(c) measures how much Irving enjoys consuming c in one period. The notebook’s figure uses the textbook’s log utility.

Each extra unit adds less utility than the one before

Model: the flow utility \(u(c) = \log c\) and its tangent. Chart adapted from Fig. 16.1 in Jones (2024), Macroeconomics, 6th ed.

How to read it: consumption c across, utility up. The blue curve is u(c) = log c. The dot is the chosen consumption level; the dashed green line is the tangent at that point, and its slope is the marginal utility u′(c) = 1/c. The slider chooses c; the title reports u(c), the marginal utility, and how much one more whole unit adds.

Do live:

1. Start at c = 2: u = 0.69, marginal utility 0.50, one more unit adds 0.41.
2. Move to c = 1: marginal utility 1.00, one more unit adds 0.69.
3. Move to c = 8: marginal utility 0.12, one more unit adds only 0.12.
4. Move to c = 0.5: utility is negative, −0.69, and the curve plunges toward zero.

Point at the tangent: it flattens as c grows.

The ninth unit adds about a sixth of what the second one did

• The answer: going from 1 to 2 adds 0.69; going from 8 to 9 adds only 0.12. Utility always rises, but by less and less.
• The slope of the curve, \(u'(c) = 1/c\), is 1 at \(c = 1\), 0.50 at \(c = 2\) and 0.125 at \(c = 8\): diminishing marginal utility.
• The log curve has no floor: as \(c\) approaches zero, utility falls without limit.

Very low consumption is very painful, so a household wants to avoid it in every period.

Numbers: the slider titles of Fig. 1 and the notebook’s “What to notice”. From 2 to 3 the gain is log 3 − log 2 = 0.41, a little less than the slope at 2, because the curve keeps flattening along the way. 0.69/0.12 ≈ 6.

Any concave curve shows diminishing marginal utility. The notebook’s Colab widget also draws the square root, u(c) = √c, with marginal utility 1/(2√c): the same shape, rising and flattening.

Why the shape is plausible: the first meal of the day matters more than the fifth; the first room of a house more than the tenth.

This is the property that drives everything in the chapter. Next: what it implies when income is uneven.

The desire to smooth

Irving earns 1 today and 5 in the future. He can spend his income in each period, or spend 3 in both. Both plans cost the same. Which one does he prefer?

Predict the gain in utility per period from the smooth plan. Then: if future income were 9 instead of 5, would the gain be larger or smaller?

Set up: β = 1 and R = 0, so the two plans cost the same: 1 + 5 = 3 + 3. The smooth plan is the average, c̄ = (c₁ + c₂)/2 = 3, which is exactly X̄/2.

Ask students to commit to a direction and, if they can, a number. Many will say “they are the same, the totals are equal”.

Because the curve bends, the smooth plan beats the uneven one

Model: log utility with \(c_1 = 1\) and \(\beta = 1\), \(R = 0\). Chart adapted from Fig. 16.2 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the same log curve as before. The two outer dots are the uneven plan, c₁ = 1 today and c₂ in the future, both on the curve. The dashed green line joins them; its midpoint (the open circle) is the average utility of the uneven plan. The filled dot in the middle, on the curve above c̄, is the utility of consuming c̄ in both periods. The slider chooses future consumption c₂; c₁ stays at 1.

Do live:

1. Start at c₂ = 5: c̄ = 3, u(c̄) = 1.10 against an average of 0.80, a gain of 0.29.
2. Move c₂ down to 1: the dashed line shrinks to a point, and the gain is 0.
3. Move c₂ up to 9: c̄ = 5, u(c̄) = 1.61 against 1.10, a gain of 0.51.

The more uneven the income, the more smoothing is worth

• The answer: \(u(\bar{c}) = \log 3 =\) 1.10 against an average utility of \(\tfrac12(\log 1 + \log 5) =\) 0.80. Smoothing adds 0.29 per period.
• With future income 9 the gain rises to 0.51; with equal incomes it is 0.
• With the less curved square-root utility the gain is only 0.11: the wish to smooth comes from the curvature of \(u\).

Diminishing marginal utility makes people spread their resources evenly over their lives.

Numbers: the slider titles of Fig. 2 and the notebook’s “What to notice”. Lifetime utility is twice these numbers, since β = 1: 2.197 with the smooth plan (the baseline cell) against 1.61 with the uneven one.

Geometric reason: for a concave curve the chord between two points lies below the curve. This is Jensen’s inequality.

This is the intuition of the permanent-income hypothesis: consumption follows an average of lifetime resources, not this period’s income. To smooth, Irving must borrow today, which he can only do if lenders trust his future income. Hold on to that thought: Act II asks what happens when he cannot.

Consumption follows lifetime resources, not this year’s paycheck

Consumption is a fixed share of income: when income is low, spending is low.

In the model, spending depends on total wealth \(\bar{X}\). The baseline Irving earns 1 but spends 3, borrowing against the 5 he will earn later. A rich retiree with no income spends out of wealth.

Earlier chapters used the simple rule as a shortcut: the Solow model’s constant saving rate, the short-run model’s consumption share of potential output. They are useful approximations for the economy as a whole, not a theory of a household.

The correction has a limit, which is the subject of Act II’s borrowing constraint: a student who cannot borrow does spend what he earns. The myth is right for some households, for the wrong reason.

Ask: give an example of someone whose spending is far above their income this year, for a good reason. (Students, people between jobs with savings, retirees, a family buying a house with a mortgage.)

The Euler equation and its lessons

Act II

At the best plan, a unit spent today is worth as much as a unit saved

\[U = u(c_{\text{today}}) + \beta\,u(c_{\text{future}})\]

\[u'(c_{\text{today}}) = \beta(1+R)\,u'(c_{\text{future}})\]

• \(\beta\) is patience: with \(\beta < 1\) the future counts less.
• A small move: save one more unit and lose \(u'(c_{\text{today}})\); it becomes \(1+R\) units, each worth \(\beta\,u'(c_{\text{future}})\).
• Only when the two are equal can no move raise \(U\): the Euler equation.

Left: the value of spending a marginal unit. Right: the value of saving it.

Assumptions 5 and 6 and step 2 of the Model overview: equations (1) and (3) of the book chapter.

The small-move argument needs no calculus. If the gain from saving one more unit is larger than the loss, Irving should save more; if smaller, he should borrow one more unit and spend it. At the best plan he is indifferent at the margin.

With calculus: substitute the budget line, c_future = (1 + R)(X̄ − c_today), into U and set the derivative with respect to c_today to zero. By the chain rule the second term contributes −β(1 + R) u′(c_future). Because u′ falls as c rises, the zero is a maximum.

If β(1 + R) = 1, the Euler equation forces u′(c_today) = u′(c_future), so equal consumption in both periods: the smoothing of Fig. 2.

With log utility, the Euler equation fixes the growth of consumption

\[\frac{1}{c_{\text{today}}} = \beta(1+R)\,\frac{1}{c_{\text{future}}} \;\Longrightarrow\; \frac{c_{\text{future}}}{c_{\text{today}}} = \beta(1+R) \;\Longrightarrow\; g_c \approx R + \log\beta\]

• Consumption grows faster with a higher \(R\) and a more patient Irving; impatience makes \(\log\beta < 0\).
• Income appears nowhere: the equation sets the slope of the path, not its level.

The budget sets how high the path is; the Euler equation sets how steep it is.

Step 3 of the Model overview: put u′(c) = 1/c into the Euler equation and multiply both sides by c_future. The left side is 1 + g_c, one plus the growth rate of consumption. Taking logs, log(1 + g_c) = log β + log(1 + R), and log(1 + x) ≈ x for small x.

The notebook’s grid-search check with R = 0.05: with β = 1, consumption grows 5 percent, exactly β(1 + R) = 1.05; with β = 0.9, consumption falls a little, since 0.9 × 1.05 = 0.945 < 1.

Ask: a very impatient person facing a low interest rate: rising or falling consumption over time? (Falling: β(1 + R) < 1.)

Irving spends a fixed share of his total wealth today: half, if he is patient

\[c_{\text{today}} = \frac{1}{1+\beta}\,\bar{X} \qquad c_{\text{future}} = \frac{\beta(1+R)}{1+\beta}\,\bar{X}\]

Baseline Irving, \(R = 0.05\)	\(c_{\text{today}}\)	\(c_{\text{future}}\)	growth \(c_{\text{future}}/c_{\text{today}}\)
patient, \(\beta = 1\)	2.881	3.025	1.050
less patient, \(\beta = 0.9\)	3.033	2.866	0.945

A computer search over every possible plan finds the same answers as the formula.

Step 4 of the Model overview: from the Euler equation, c_future = β(1 + R) c_today. Substitute into the lifetime budget; the factor 1 + R cancels; (1 + β) c_today = X̄. The textbook solves the case β = 1, where Irving spends half of his total wealth today.

Numbers: the notebook’s Check 1. Grid search with 100,001 candidate values of c_today: 2.8810 for β = 1 and 3.0326 for β = 0.9, equal to the formula X̄/(1 + β) with X̄ = 5.7619. The future values: 1.05 × 2.881 = 3.025 and 0.945 × 3.0326 = 2.866. Both sides of the Euler equation are equal (0.3471 and 0.3298).

Check the budget for β = 1: Irving borrows 2.881 − 1 = 1.881 and repays 1.05 × 1.881 = 1.975, leaving 5 − 1.975 = 3.025 to spend.

With log utility, the share 1/(1 + β) does not depend on R or on the timing of income.

Interest rates and growth rates are numbers of the same size

\[1+R = \frac{1+g_c}{\beta} \qquad\Longrightarrow\qquad R = \frac{1+g_c}{\beta} - 1\]

Consumption grows 2% a year	\(R\) required	log approximation \(g_c - \log\beta\)
\(\beta = 1\)	2.00%	2.00%
\(\beta = 0.99\)	3.03%	3.01%

Growth models set how fast consumption grows; the Euler equation then says which real interest rate households need to accept that path.

Step 5 of the Model overview, equation (7). For one household, R is given and it chooses the growth of consumption. For the economy, the logic runs the other way: the Solow–Romer model of Chapter 6 pins down growth, and the Euler equation gives the interest rate that makes households content with that path.

Numbers: the notebook’s Check 2. With β = 1, R = 1.02 − 1 = 2.00 percent. With β = 0.99, R = 1.02/0.99 − 1 = 3.03 percent; the approximation gives 3.01. Plugged back in, both give consumption growth of 2.00 percent.

The premium for impatience is about −log β per year, small because β is close to 1. Faster growth raises the required interest rate roughly one for one.

Ask: if growth slowed permanently from 2 to 1 percent a year, what would the model predict for real interest rates? (About one point lower.) This is one reading of the low real rates of the 2010s.

Each input moves consumption by a predictable amount

A change in …	\(c_{\text{today}}\)	\(c_{\text{future}}\)	baseline (\(\beta = 1\), \(R = 0.05\))	the budget line
\(y_{\text{today}}\) or \(f_{\text{today}}\), +1	\(+\frac{1}{1+\beta}\)	\(+\frac{\beta(1+R)}{1+\beta}\)	+0.5 and +0.525	shifts out
\(y_{\text{future}}\), +1	\(+\frac{1}{(1+\beta)(1+R)}\)	\(+\frac{\beta}{1+\beta}\)	+0.476 and +0.5	shifts out
\(1+R\), +1%	\(-\sigma\) %	\(+(1-\sigma)\) %	−0.83% and +0.17%	pivots
\(\beta\), +1%	\(-\frac{\beta}{1+\beta}\) %	\(+\frac{1}{1+\beta}\) %	−0.5% and +0.5%	does not move

The marginal propensity to consume out of a windfall today is one half: the rest is saved for the future.

The Model overview’s comparative statics table. Income and wealth enter X̄ linearly, so their effects are constants: the marginal propensities to consume. For R and β, take logs of the solution.

σ is the share of total wealth that comes from future income: σ = 4.762/5.762 = 0.826 at baseline. A 1 percent rise in 1 + R lowers the present value of future income by about 1 percent, and so X̄ by about σ percent.

The notebook’s Check 3 confirms the elasticities with a 1 percent change: c_today −0.818 percent (predicted −0.826), c_future +0.174 (predicted +0.174), and a 1 percent higher β lowers c_today by 0.498 percent (predicted 0.500). An elasticity is exact only for very small changes.

The two elasticities for 1 + R differ by exactly 1, as the Euler equation requires. The budget line pivots around the no-borrowing point, c_today = f_today + y_today and c_future = y_future, which is affordable at any interest rate.

A higher interest rate pulls in three directions

• Wealth effect: future income is worth less today, so \(\bar{X}\) and \(c_{\text{today}}\) fall.
• Substitution effect: consumption today gets dearer (\(1+R\)), so spending shifts to the future.
• Income effect: a saver earns more and can afford more in both periods.

All wealth financial, \(f_{\text{today}} = 6\)	\(R = 0\)	\(R = 0.05\)	\(R = 0.10\)
\(c_{\text{today}}\), log utility	3.000	3.000	3.000
\(c_{\text{today}}\), square root	3.000	2.927	2.857

With log utility the substitution and income effects cancel exactly; with other utility functions either one can win.

Step 6 of the Model overview. With log utility, c_today = X̄/(1 + β) and R works only through X̄: the wealth effect. Take an Irving whose wealth is all financial: X̄ = f_today does not depend on R, and neither does c_today. So the other two effects must cancel.

With square-root utility the Euler equation gives c_future/c_today = β²(1 + R)², and c_today = X̄/[1 + β²(1 + R)]. Now R is in the denominator, and a higher R lowers c_today even with X̄ fixed: the substitution effect wins.

Numbers: the notebook’s Check 4. For the baseline Irving at R = 0.05, square-root utility gives c_today = 2.8107 (grid search and formula agree), a little below log utility’s 2.881.

The sign of the effect of R on consumption today is an empirical question. This matters for monetary policy: Chapter 11’s IS curve assumes higher rates cut spending, and the wealth and substitution effects are two reasons why.

Higher interest rates do not always make people save more

If saving pays more, everyone saves more.

A saver who lives off financial wealth is also richer when rates rise. With log utility the two pulls cancel: at \(R\) = 0, 5% or 10%, he spends 3.000 today. For a borrower with future income, the wealth effect lowers spending today.

The common intuition is the substitution effect alone. The income effect pushes the other way for anyone who is a net saver: a retiree living on interest income can spend more in every period when rates rise.

Numbers: the notebook’s Check 4 (log utility, f_today = 6, no labor income).

For policy students: the evidence on how household saving responds to the interest rate is mixed, which is one reason tax incentives for saving often move savings between accounts more than they raise total saving.

With many periods, Irving consumes his permanent income

\[c = \frac{\bar{X}}{T} = \frac{f_{\text{today}} + y_1 + y_2 + \dots + y_T}{T}\]

• With \(R = 0\), \(\beta = 1\): consumption is flat.
• A temporary extra unit raises spending by \(1/T\).
• A permanent raise lifts spending by about 1.

Periods of life left	MPC out of a windfall
2	0.500
3	0.333
50	0.020
80	0.013

Friedman’s permanent-income hypothesis: temporary income changes barely move consumption.

The second block of the Model overview, equation (8). The Euler equation holds between every pair of neighboring periods, so with β(1 + R) = 1 consumption is the same number c in every period. With R = 0 the lifetime budget is a plain sum.

Numbers: the notebook’s MPC-by-T loop (1/2, 1/3, 1/50, 1/80) and Check 5: a one-time extra 0.01 for a consumer with 60 periods raises consumption by 0.01/60, an MPC of 0.0167 = 1/60.

A further prediction: an anticipated raise does not move consumption on the day it is paid, because it was already part of X̄. The random walk slide returns to this.

Friedman, M. (1957), A Theory of the Consumption Function, Princeton University Press.

Saving for retirement makes wealth rise and fall over a life

• Work \(W = 40\) periods at income 1, then retire for 20: \(T = 60\).
• Consume \(c = 40/60 =\) 0.667 in every period.
• Save 0.333 a year while working, and spend down in retirement.

\[\text{peak wealth} = W\cdot\frac{y\,(T-W)}{T} = \text{13.3}\]

More than 13 years of income, on the day he retires; zero at the end of life.

Modigliani’s life-cycle hypothesis: flat consumption plus a hump in income gives a hump in wealth.

Step 3 of the second block of the Model overview. By equation (8), c = Wy/T. While working, Irving saves y − c = y(T − W)/T per period; his wealth climbs to W times that on the day he retires, then falls to zero in the last period.

Numbers: the notebook’s Check 5: consumption 0.667, saving while working 0.333, peak wealth 13.33 (formula 13.33), wealth at the end 0.000000.

This prediction is tested in Act III: Japan’s households saved 12.8 percent of income in 1994 and 0.7 percent in 2024, as the population aged.

Modigliani, F. and R. Brumberg (1954), in Post-Keynesian Economics (K. Kurihara, ed.), Rutgers University Press.

A household that cannot borrow spends what it has

\[c_{\text{today}} = \min\left\{\frac{\bar{X}}{1+\beta},\; f_{\text{today}} + y_{\text{today}}\right\}\]

• The limit binds when the present value of future income exceeds what Irving has today: \(\frac{y_{\text{future}}}{1+R} > f_{\text{today}} + y_{\text{today}}\).
• Baseline Irving: \(4.76 > 1\). He spends 1 instead of 2.881, and 5 in the future.
• An Irving with income 4 today and 2 later wants to save anyway: the limit does not bind, and he spends 2.952.

When the limit binds, consumption tracks current income.

The third block of the Model overview, equation (9). The constraint f_future ≥ 0 means c_today ≤ f_today + y_today. When the unconstrained plan is affordable, it is still the best. When it is not, Irving gets as close as he can by spending everything he has today.

Numbers: the notebook’s Check 6: baseline plan 2.881, cash 1.000, binds: True, c_today = 1.000; second Irving (y_today 4, y_future 2): plan 2.952, cash 4.000, binds: False.

Why can’t people borrow? No collateral, a bad credit history, or a financial crisis that shuts lenders down (Chapter 10). Students can borrow for tuition, but rarely for rent at the rate a bank pays on deposits.

Whether a household can borrow decides its marginal propensity to consume

Irving receives …	MPC, can borrow	MPC, cannot borrow
100 dollars more income today	0.5	1.0
100 dollars more income in the future	0.476	0.0
100 dollars more financial wealth	0.5	1.0
a tax cut today, paid by a tax rise later	0.0	1.0

The same 100 dollars can be half spent, all spent or not spent at all, depending on who gets it and how it is paid for.

The notebook’s MPC table (Key numbers after Fig. 2): each version of the baseline Irving gets 0.01 more, 100 dollars when one unit is 10,000 dollars, with R = 0.05. The textbook’s number: 100 extra dollars raise consumption by 50 when Irving can borrow.

Future income counts for a little less, 0.5/1.05 = 0.476, because it is discounted.

The constrained Irving spends every extra dollar he gets today, including the tax cut, and gains nothing today from extra future income.

The last row is Ricardian equivalence, the next slide. With a mix of both kinds of households, the economy’s average MPC lies between the two columns.

The timing of taxes does not matter, for a household that can borrow

\[\Delta\bar{X} = +\Delta - \frac{(1+R)\,\Delta}{1+R} = 0\]

• Cut today’s tax by \(\Delta\), borrow, and raise the future tax by \((1+R)\Delta\).
• Total wealth is unchanged, so Irving saves the whole tax cut: Ricardian equivalence.
• It fails if households are constrained, or if later taxes fall on others, such as future generations.

For a given path of government spending, a debt-financed tax cut is a loan, not a gift.

The third block of the Model overview. With taxes, incomes in the budgets are after tax, and X̄ = f_today + (y_today − τ_today) + (y_future − τ_future)/(1 + R). The government borrows and lends at the same rate R as Irving.

Numbers: the notebook’s Check 6: a tax cut of 0.01, repaid with interest, leaves total wealth at 5.761905 before and after.

The name: David Ricardo discussed the idea in the early 1800s (and doubted it held in practice); Barro (1974, Journal of Political Economy) gave it its modern form, with families that care about their heirs, so even taxes on the next generation count.

Chapter 18 returns to government debt.

If all news is already in consumption, only surprises move it

\[u'(c_{\text{today}}) = \beta(1+R)\;E\big[u'(c_{\text{future}})\big]\]

• With uncertain income, the expected marginal utility of the future must balance.
• With \(\beta(1+R) = 1\) and nearly straight marginal utility: \(c_{\text{future}} = c_{\text{today}} + \text{surprise}\).
• An expected promotion moves spending when it is announced, not when it is paid. An unexpected job loss moves it a lot.

Hall’s random walk: changes in consumption should be hard to predict.

The third block of the Model overview. E[·] is the average over the possible outcomes.

Hall, R. E. (1978), Journal of Political Economy: if households use all they know, past information cannot predict the change in consumption, apart from the trend set by the interest rate.

A famous test, in the textbook’s case study: spending falls sharply at retirement, an event everyone anticipates. Aguiar and Hurst (2005, Journal of Political Economy) used food diaries and found that the food people actually eat does not fall; retirees spend more time shopping and cooking and pay less for the same meals. Consumption and expenditure are not the same thing.

Ask: name an anticipated change in your income. Did your spending change when it arrived?

Risk makes people save, even when their income is low

\[\frac{1}{c_{\text{today}}} = \frac{1}{2}\cdot\frac{1}{4 - c_{\text{today}}} + \frac{1}{2}\cdot\frac{1}{8 - c_{\text{today}}}\]

• Future income is 3 or 7 with equal chance, instead of a sure 5. The average is the same.
• Marginal utility \(1/c\) is steeper at low consumption: the bad outcome weighs more than the good one.
• Consumption today falls from 3 to 2.44: a precautionary saving of 0.56.

Precautionary savers act much like constrained households: their spending follows their current income closely.

The worked example of the Model overview with R = 0, β = 1 and the baseline incomes. In the bad case c_future = 3 + (1 − c_today) = 4 − c_today; in the good case 8 − c_today. Multiply out: c² − 9c + 16 = 0, whose root below 4 is (9 − √17)/2 = 2.4384.

Numbers: the notebook’s Check 7: grid search 2.4384; precautionary saving 0.5616; both sides of the expected Euler equation 0.4101.

The textbook links it to the 2008–09 crisis: saving rose as fear of job loss rose. Fig. 4 shows it. Carroll (1997, Quarterly Journal of Economics) shows that with income risk many households keep a small “buffer stock” of savings and behave like hand-to-mouth consumers in between.

This closes Act II. Next: what the data say about debt, saving and wealth.

Debt, saving and wealth in the data

Act III

Household debt

How much have U.S. households borrowed, relative to the size of the economy, since 1970?

Ask: in 1970, was the debt of U.S. households closer to a quarter, a half or all of a year’s GDP? And at the peak? Collect guesses.

U.S. household debt doubled relative to GDP before 2008, then fell

Data: Federal Reserve Board, Financial Accounts of the United States, household debt (CMDEBT); BEA, GDP (GDP), via FRED. Chart inspired by Fig. 16.3 in Jones (2024), Macroeconomics, 6th ed.

How to read it: the debt of U.S. households and nonprofit organizations (mostly mortgages, plus consumer credit), divided by nominal GDP, in percent, quarterly since 1970. The arrow marks the peak. Hover to read any quarter.

Point at three phases: below 50 percent until the mid-1980s; a steady climb, then a steep one in the 2000s housing boom; the fall after 2008 as households paid down debt or defaulted.

Point at 2020: the jump is a GDP effect. Output collapsed in the pandemic while debt did not.

Debt peaked at 98% of GDP and is now back at the level of the late 1990s

• At most 48.4% of GDP before 1985; 68.8% in 2000; a peak of 98.0% in 2008Q1. The 2008 average was 2.28 times the 1970 average.
• Households then deleveraged: 77.7% in 2014, 72.8% in 2019, 65.7% in 2026Q2.
• In the model, borrowing against future income is rational. The question is what Irving expected his future income, and his house, to be worth.

The boom in household debt was one half of the balance-sheet crisis of Chapter 10.

Numbers: the notebook’s Fig. 3 key numbers. The textbook says “about 67 percent” in 2000 (our 68.8) and “nearly 100 percent by 2009” (our peak 98.0 in 2008Q1, 97.1 on average in 2009).

Data hygiene, a teaching moment from the notebook (its second chart for Fig. 3, not shown here): FRED now reports this debt series in millions of dollars but GDP in billions, so a naive ratio gives 42,928 percent in 1970Q1. Always check units. And the 2023 revision of GDP lowered the ratio after 2000 by up to 3.2 points: a larger denominator, a smaller ratio.

Mian, Rao and Sufi (2013, Quarterly Journal of Economics) show that the U.S. counties that lost the most housing wealth in the bust, above all those with highly indebted households, cut their spending most.

Household debt around the world

Did households in other countries also borrow heavily before 2008, and then pay it down?

Ask: name a country whose households you think owe more than a year of GDP today. Collect two or three guesses before the chart.

Some countries deleveraged after 2008; others kept borrowing

Data: Bank for International Settlements, total credit statistics, credit to households and NPISHs, percent of GDP (WS_TC). Chart inspired by Fig. 16.3 in Jones (2024), Macroeconomics, 6th ed.

How to read it: household debt in percent of GDP for 43 countries, quarterly, from the BIS. The chart opens on the United States; the buttons show a group (the G7, a region, all), and a click on a country in the legend adds or removes it. The axis widens to 140 percent when needed.

Do live:

1. “Textbook”: the U.S. BIS series peaks at 98.4 percent in 2007Q4 and is 67.2 percent in 2026Q1, on average 1.3 points above the Federal Reserve ratio.
2. Add Spain and Ireland from the legend: big booms and big deleveraging.
3. Click “All”, then point at Australia, Switzerland and Canada at the top, and China rising from the bottom.

Spain and Ireland paid down their debts; Australia and Canada did not

• Spain fell from 85.7% of GDP (2010Q2) to 42.5%; Ireland from 117.4% (2009Q4) to 26.3%.
• Part of Ireland’s fall is a GDP effect: multinational profits booked there inflate its GDP. Look at the denominator.
• Households in Switzerland (127.0%), Australia (114.1%) and Canada (100.0%) owe more than a year of GDP. China’s ratio rose from 11.3% in 2006 to 57.5%.

A ratio to GDP can fall because debt fell or because GDP rose: always check both.

Numbers: the notebook’s “Beyond the United States” notes for Fig. 3.

Countries with high and rising ratios had long house-price booms without a bust of the U.S. kind. High debt is not by itself a crisis: what matters is who holds it, at what interest rate, and what happens to house prices and incomes.

For policy students: several of these countries (Canada, Australia, Sweden) tightened mortgage rules in the 2010s, such as limits on loan-to-value ratios, to slow household borrowing.

The personal saving rate

What share of their disposable income have U.S. households saved since 1970?

The personal saving rate is personal saving divided by disposable income, income after taxes. Ask: is it closer to 2, 10 or 25 percent today? What happened in 2020?

U.S. households saved less and less for two decades

Data: BEA, Personal Saving Rate (PSAVERT), via FRED; quarterly values are averages of the monthly data. Chart inspired by Fig. 16.4 in Jones (2024), Macroeconomics, 6th ed.

How to read it: personal saving as a percent of disposable income. The buttons switch between quarterly averages (as in the textbook) and the monthly data; the title reports the highest and lowest values.

Do live:

1. “quarterly”: highest 24.2 percent in 2020Q2, lowest 1.8 percent in 2005Q3.
2. “monthly”: highest 31.8 percent in April 2020, lowest 1.4 percent in July 2005. Monthly data are noisier; averaging over a quarter smooths out the extremes.
3. Back to quarterly: point at the slide from the early 1980s to 2005, and at the rise after 2008.

Saving fell from 12% to 2.5%, then rose in the crisis and in the pandemic

• 12.2% on average in the 1970s and 11.2% in 1980–84; 2.5% in 2005–07, during the housing boom.
• After 2008 saving rose as households rebuilt their balance sheets: precautionary saving at work.
• In 2020 it shot up, since many purchases were impossible and transfers raised income. It fell to 2.6% in mid-2022 and is 4.4% in 2026Q2.

Saving rates move with fear and with what can be bought, not only with income.

Numbers: the notebook’s Fig. 4 key numbers. The textbook says “more than 10 percent” in the 1970s and early 1980s and “around 3 percent” by the mid-2000s. The values after 2000 are up to about 2 points lower than in the textbook’s figure, because the 2023 revision of the national accounts lowered measured saving: the low is now closer to 2.5 percent. The textbook exercise’s 2007 average of the months: 2.5 percent.

The pandemic saving is not a precautionary story alone: travel, restaurants and services were closed, so forced saving played a big role. Then the excess savings were spent in 2021–22, one of the explanations of the inflation of Chapter 10.

Latest month: 4.1 percent in August 2026.

Saving across countries

According to the permanent-income view, households that expect to be much richer soon should borrow and save little.

China’s economy has grown faster than almost any other for decades. Predict: do Chinese households save more or less of their income than American households, and by how much?

Ask students to commit to “more” or “less”, and to a number. The model’s logic says: fast-growing income means high human wealth relative to today’s income, so a household should borrow against its future, like the baseline Irving.

Saving rates differ hugely across countries, and China’s is the highest

Data: OECD, National Accounts at a Glance, net household saving, percent of net disposable income (DSD_NAAG@DF_NAAG_V, B8NS1M). Chart inspired by Fig. 16.4 in Jones (2024), Macroeconomics, 6th ed.

How to read it: annual net household saving as a percent of net disposable income, from the OECD, for 35 countries. It is close to the BEA’s definition: for the U.S. the OECD’s rate is on average 0.2 points above the yearly average of the monthly BEA data. The chart opens on the U.S.; the buttons show groups; the legend adds or removes a country. The zero line marks dissaving.

Do live:

1. Add China from the legend: the reveal.
2. Add Japan: the long fall.
3. Add Germany and France: steady high saving.
4. Add Greece: below zero since the debt crisis.

China saves more than a third of its income: the model gets the facts backward

• The answer: far more. Chinese households save 28% to 39% of income since 1992, 34.9% in 2023; the U.S. rate fell to 2.3% in 2005.
• Japan saved 12.8% in 1994 and 0.7% in 2024 as it aged: retirees spend down, as the life cycle predicts.
• Germany and France: 8% to 16% every year since 1995. Greece: −16.5% in 2013, living on wealth.

The fall in U.S. saving was not a world trend, and the permanent-income view alone cannot explain China.

Numbers: the notebook’s “Beyond the United States” notes for Fig. 4 (OECD data). In 2020 saving rose in almost every country, by 8 to 12 points in the U.S., Japan, the U.K. and Canada: a pandemic effect, not only U.S. policy.

Why does China save so much? Candidate explanations, all debated: a thin social safety net and high costs of health care and education (precautionary saving; Chamon and Prasad, 2010, American Economic Journal: Macroeconomics); the one-child policy and rising sex ratios, with families saving to improve their sons’ marriage prospects (Wei and Zhang, 2011, Journal of Political Economy); and borrowing constraints in an underdeveloped credit market. The textbook returns to the puzzle in Chapter 19, on trade.

Household wealth

U.S. households borrowed more and saved less for decades. Did they get poorer, relative to their income?

Net worth is everything households own (houses, stocks, bonds, deposits) minus everything they owe. Ask: compared with 1970, is household net worth today a smaller or a larger multiple of a year’s income?

Yet U.S. household wealth rose from 5 to more than 8 years of income

Data: Federal Reserve Board, Financial Accounts of the United States, household and nonprofit net worth as a percent of disposable income (HNONWPDPI), via FRED. Chart inspired by Fig. 16.5 in Jones (2024), Macroeconomics, 6th ed.

How to read it: household net worth divided by one year of disposable income, quarterly. A value of 5 means households own five years of income. Three arrows mark turning points: the dot-com peak, the housing peak and the financial crisis.

Point at the rise of the late 1990s (stock prices), the housing boom and bust, and the climb since 2012 to a new high.

Wealth rose with stock and house prices, even as saving fell

• About 5 years of income in 1970, about 6 at the end of the 1990s; 6.76 at the housing peak, 5.45 in the crisis.
• Since 2012 it has climbed, with dips in 2020 and 2022, to 8.28 in 2026Q2.
• Wealth can grow by saving, or by capital gains on what you already own. In the model, a higher \(\bar{X}\) means more spending.

Households that felt richer from rising asset prices had less reason to save out of income.

Numbers: the notebook’s Fig. 5 “What to notice” and title (5.0 to 8.3).

The textbook’s explanation: the balance of your 401(k) can rise because you save more each month, or because the assets in it gain value. The stock booms of the 1980s and 1990s and the housing boom before 2008 may have made households feel rich enough to save less and borrow more.

A caveat: capital gains on houses are partly a gain for owners and a loss for future buyers, who must pay more. The economy as a whole is not richer because the price of the existing stock of houses rises.

A low saving rate does not mean households are getting poorer

Americans save almost nothing, so their wealth must be shrinking.

Saving is a flow out of income; wealth is a stock that also moves with asset prices. In 2005–07 the saving rate was 2.5%, yet net worth reached 6.76 years of income at the housing peak.

The distinction between stocks and flows recurs throughout the book: debt versus the deficit (Chapter 1), capital versus investment (Chapter 5).

The other side: wealth that rests on asset prices can vanish fast. In the crisis the ratio fell from 6.76 to 5.45, and households then saved more (Fig. 4). Wealth is also very unequally distributed: a high aggregate ratio says nothing about the typical household’s buffer.

Wealth and saving together

If households save less when they feel wealthy, what should a chart of saving against wealth look like?

Each point will be one quarter since 1970: wealth across, the saving rate up. Predict the sign of the correlation, and whether the 2020s fit the pattern.

Ask students to sketch the cloud on paper: upward, downward, or flat. And where the pandemic quarters will sit.

Households saved less when they were wealthier

Data: Federal Reserve Board (HNONWPDPI) and BEA (PSAVERT), via FRED. Chart inspired by Figs. 16.4 and 16.5 in Jones (2024), Macroeconomics, 6th ed.

How to read it: one point per quarter, wealth (net worth over disposable income) across, the personal saving rate up, colored by decade. The line is the best-fitting straight line through all the points. Hover for the quarter; click a decade in the legend to hide it.

Do live:

1. Point at the 1970s and 1980s at the upper left, and the 2000s and 2010s at the lower right.
2. Click “2020s” in the legend to hide it: the downward cloud is clearer.

The cloud slopes down, but a correlation is not a cause

• The answer: negative. Over 226 quarters the correlation between saving and wealth is −0.56.
• The 2020s sit high on both axes: pandemic saving had little to do with wealth.
• A second reading: households borrow against a higher expected income. But that story predicts low saving in fast-growing China.

The wealth effect fits the U.S. facts; other forces, from credit to demography, move saving too.

Numbers: the notebook’s merge of the saving and wealth series: 226 quarters, correlation −0.56.

Why a correlation is not proof: both series respond to other forces. Easier credit (mortgage refinancing, home-equity loans) raises house prices and lets households spend more at the same time. An aging population, interest rates and the share of income going to high savers also move both.

Mian, Rao and Sufi (2013) is one attempt to isolate the wealth effect, using differences across U.S. counties in the house-price bust.

Household wealth around the world

Did household wealth rise relative to income in other countries too, or only in the United States?

Ask: which country do you expect had the largest housing-driven rise in wealth before 2008? Collect guesses (Spain, Ireland, the U.K. are common).

Wealth rose relative to income almost everywhere

Data: OECD, National Accounts at a Glance, household balance sheets: net financial worth, dwellings and land over disposable income (DSD_NAAG@DF_NAAG_V). Chart inspired by Fig. 16.5 in Jones (2024), Macroeconomics, 6th ed.

How to read it: annual household net worth (net financial worth plus dwellings and the land under them) in years of disposable income, for 26 OECD countries, from 1995 at the earliest. For the U.S. it is within 9 percent of the Federal Reserve ratio of Fig. 5. The chart opens on the U.S.; buttons and legend add countries; the axis widens when a country leaves the 3-to-9 range.

Do live:

1. Add Spain: a boom and a bust.
2. Add Sweden and Denmark: a long climb.
3. Add the United Kingdom: a sharp fall after 2020.

Housing booms raised wealth fast, and higher interest rates cut it

• Spain: 6.0 years of income in 1995, 11.6 in 2007, 8.9 in 2012. The U.S. peaked at only 6.9 before the crisis.
• Sweden: from 2.8 in 1995 to 10.2 in 2021; Denmark to 12.3. In 2022, when interest rates jumped, these ratios fell.
• The U.K.: from 8.8 in 2020 to 6.0 in 2024, much of it lower values of pension entitlements as rates rose.

Wealth is measured at market prices, so it moves with interest rates and asset prices, not only with saving.

Numbers: the notebook’s “Beyond the United States” notes for Fig. 5.

The link to the model: a higher interest rate lowers the present value of future income (human wealth) and, through asset prices, of houses, stocks and pensions (financial wealth). Both are wealth effects that lower consumption: one channel of monetary policy in Chapter 12.

Data lesson: the U.K. drop is partly an accounting change in the value of defined-benefit pension promises, which are discounted at market interest rates.

Should stimulus checks go to the households that cannot borrow?

In a recession, Congress sends checks to households. Who should get them, if the goal is to raise spending fast?

What the model predicts

• Those who can borrow spend half, or \(1/T\).
• Constrained households spend all of it.
• So target low-wealth households.

What it leaves out

• Some rich homeowners hold no cash.
• Targeting takes time and data.
• The average MPC is contested.

The model’s numbers are the MPC table: 0.5 when Irving can borrow, 1.0 when he cannot; 1/T with many periods.

The evidence. Johnson, Parker and Souleles (2006, American Economic Review) use the random timing of the 2001 tax rebate checks and find that households spent a sizeable share on nondurable goods within months of receipt, far more than the permanent-income model predicts, and most among households with little liquid wealth. Parker, Souleles, Johnson and McClelland (2013, American Economic Review) find similar responses to the 2008 stimulus payments, with large additional spending on durables such as cars. Kaplan and Violante (2014, Econometrica) explain why: many households own houses or retirement accounts but keep little cash, so they behave as if constrained. Shapiro and Slemrod (2003, American Economic Review) asked households directly in 2001, and only a minority said they would mostly spend the rebate. The size of the average MPC is contested.

Ask the policy students: a flat check to everyone or a larger check to fewer households? What do you gain and lose?

Does a tax cut paid for by borrowing raise spending?

The government cuts taxes today and borrows; taxes must rise later. Will households spend the tax cut?

What the model predicts

• If households can borrow and pay the later taxes: no. Total wealth \(\bar{X}\) does not change.
• If they are constrained: they spend it all.

What it leaves out

• Later taxes may fall on other people, or on the next generation.
• Households may not see, or believe, the future tax rise.
• Evidence on full Ricardian saving is weak.

The model: Ricardian equivalence (the eqpanel slide) and the last row of the MPC table: 0.0 when Irving can borrow, 1.0 when he cannot.

The research. Barro (1974, Journal of Political Economy) argued that if parents care about their children, even taxes on the next generation count, so government bonds are not net wealth. Bernheim (1987, NBER Macroeconomics Annual) reviews the theory and the evidence and finds strong reasons to doubt full equivalence. The rebate studies of the previous slide also reject full Ricardian behavior for many households. Still, few economists think the offset is zero: some households do save tax cuts they expect to be reversed.

Chapter 18 returns to government debt and deficits.

Ask the policy students: would you expect more Ricardian behavior from a government with a high debt, or a low one? (Arguably from a high one: households can see the future tax bill coming.)

Should saving for retirement be the default?

Many workers reach retirement with little saved. Should employers enroll them in a pension plan unless they opt out?

What the model predicts

• A life-cycle saver builds wealth while working and spends it in retirement.
• A default should not matter: a rational saver picks the same plan.

What the evidence shows

• Defaults matter a lot: inertia keeps people where they start.
• Present bias: people plan to save, but tomorrow.
• A default can also lock people into a low rate.

The model: the life-cycle check (save 0.333 a year for 40 years; peak wealth 13.3 years of income). In the model the default enrollment of a plan is irrelevant.

The research. Madrian and Shea (2001, Quarterly Journal of Economics) studied a U.S. firm that switched new hires to automatic enrollment in its 401(k) plan: participation jumped to nearly everyone, but many workers stayed at the default contribution rate and default fund. Thaler and Benartzi (2004, Journal of Political Economy) designed “Save More Tomorrow”, in which workers commit in advance to save part of future raises; saving rates rose sharply. Laibson (1997, Quarterly Journal of Economics) models present bias: people are especially impatient about the present, so they borrow too much and save too little by their own standards. Chetty, Friedman, Leth-Petersen, Nielsen and Olsen (2014, Quarterly Journal of Economics) find in Danish data that most people are passive: automatic contributions raise total saving, while tax subsidies mostly move savings between accounts.

The U.K. made automatic pension enrollment national law in 2012 (“auto-enrolment”); the U.S. SECURE 2.0 Act of 2022 requires it for many new plans.

Ask the policy students: is a default a gentle nudge or a paternalistic choice? Who sets the default rate?

“No one solves an Euler equation”

A skeptic says: “Real people don’t compute present values or marginal utilities. They spend their paycheck, borrow on credit cards at punishing rates, and forget to save. A model of a perfect planner is useless.”

Reply: the model is the benchmark that makes the departures measurable. Wealthy households smooth much as it predicts. The big deviations, high MPCs and too little saving, come from borrowing limits, risk and present bias, each a small change to the same model. Without the benchmark we could not tell a constraint from a mistake.

Take the objection seriously: behavioral economics documents real departures (the textbook’s case study). People borrow at high credit-card rates while holding low-yield savings; defaults and framing change saving (Madrian and Shea, 2001); Laibson’s (1997) present bias makes spending sensitive to income.

The reply rests on Act II: a borrowing constraint (equation 9), precautionary saving (the 3 → 2.44 example) and present bias are all modifications of the same lifetime problem, and they explain why MPCs are high for low-wealth households. The textbook’s summary of the household evidence: the permanent-income model describes well-off households well; many poorer households have a high MPC; and households are heterogeneous.

Like the Solow model for growth, the neoclassical consumption model is a workhorse: wrong in details, right in its main logic (consumption follows lifetime resources), and the base on which richer models are built.

Ask: name one of your own spending decisions that the model explains well, and one it does not.

What to remember from this chapter

• The lifetime budget: the present value of spending equals total wealth, financial plus human: \(\bar{X}\).
• Diminishing marginal utility makes people smooth. At the best plan the Euler equation holds; with log utility, \(c_{\text{today}} = \bar{X}/(1+\beta)\).
• Interest rates track growth: 2% growth needs \(R\) of 2%, or about 3% with \(\beta = 0.99\).
• The MPC is \(1/T\) for those who can borrow and 1 for those who cannot; Ricardian equivalence holds only for the first.
• In the data: debt rose to 98% of GDP, saving fell to 2.5%, and wealth rose to 8.3 years of income.

Ask each student to write one sentence answering the opening question: how do households decide how much to spend today and how much to save? A good answer: they spend a share of their lifetime wealth, so they borrow when young or temporarily poor and save the rest of a windfall, unless they cannot borrow or fear a fall in income, in which case they spend what they have.

For the policy students, three habits: ask whether an income change is temporary or permanent; ask whether the people who receive it can borrow; and ask who pays the bill later.

Walk the three branches of the mind map in about a minute each: a lifetime budget (cyan), the Euler equation and its lessons (lavender), debt, saving and wealth in the data (green). Click the image to zoom in.

Households spend out of lifetime wealth; borrowing limits and risk decide who spends the next dollar

Next: Chapter 17, Investment

This chapter turned consumption from a fixed share of income into a choice over a lifetime. The next chapter does the same for the other big private spending decision: investment by firms, which compare the return on new capital with the real interest rate, the same price that appeared in the Euler equation.

Sources: data and figures

• Figs. 1 and 2, utility and smoothing. Model figures: log utility, the baseline Irving of the book chapter. Adapted from Figs. 16.1 and 16.2 in Jones (2024).
• Fig. 3, household debt. Federal Reserve Board, Financial Accounts of the United States (Z.1, table B.101), CMDEBT; BEA, GDP, via FRED; BIS total credit statistics (WS_TC) for 43 countries. Inspired by Fig. 16.3 in Jones (2024).
• Fig. 4, saving. BEA, Personal Saving Rate (PSAVERT), via FRED; OECD, National Accounts at a Glance (DSD_NAAG@DF_NAAG_V, B8NS1M), OECD Data Explorer, for 35 countries. Inspired by Fig. 16.4 in Jones (2024).
• Fig. 5, wealth. Federal Reserve Board, HNONWPDPI, via FRED; OECD household balance sheets (LES1M_BF90_POP, LES1M_N111N_POP, LES1M_N211N_POP, B6GS1M_POP) for 26 countries. Inspired by Figs. 16.4 and 16.5 in Jones (2024).
• Textbook. Jones, C. I. (2024). Macroeconomics, 6th ed. W. W. Norton. Book chapter, with the data, code, derivations and every figure: Data Science and Macroeconomic Models, Chapter 16.

Sources: research cited

• Consumption theory. Friedman, M. (1957), A Theory of the Consumption Function, Princeton University Press; Modigliani, F. and R. Brumberg (1954), in K. Kurihara (ed.), Post-Keynesian Economics, Rutgers University Press; Hall, R. E. (1978), Journal of Political Economy 86(6); Carroll, C. D. (1997), Quarterly Journal of Economics 112(1); Aguiar, M. and E. Hurst (2005), Journal of Political Economy 113(5).
• Stimulus and the MPC. Johnson, D. S., J. A. Parker and N. S. Souleles (2006), American Economic Review 96(5); Parker, J. A., N. S. Souleles, D. S. Johnson and R. McClelland (2013), American Economic Review 103(6); Kaplan, G. and G. L. Violante (2014), Econometrica 82(4); Shapiro, M. D. and J. Slemrod (2003), American Economic Review 93(1).
• Ricardian equivalence. Barro, R. J. (1974), Journal of Political Economy 82(6); Bernheim, B. D. (1987), NBER Macroeconomics Annual 2.
• Saving behavior. Laibson, D. (1997), Quarterly Journal of Economics 112(2); Madrian, B. C. and D. F. Shea (2001), Quarterly Journal of Economics 116(4); Thaler, R. H. and S. Benartzi (2004), Journal of Political Economy 112(S1); Chetty, R., J. N. Friedman, S. Leth-Petersen, T. H. Nielsen and T. Olsen (2014), Quarterly Journal of Economics 129(3).
• Wealth and China. Mian, A., K. Rao and A. Sufi (2013), Quarterly Journal of Economics 128(4); Chamon, M. D. and E. S. Prasad (2010), American Economic Journal: Macroeconomics 2(1); Wei, S.-J. and X. Zhang (2011), Journal of Political Economy 119(3).